AUGUSTA, Maine — He has compared the IRS to the Gestapo, accused a political enemy of having “no brains” and a “black heart,” and said critics of his decision to skip an NAACP event should “kiss my butt.”

Governor Paul LePage won election in 2010 running as a brash and provocative outsider, but now, as the Republican prepares to seek a second term, there are signs his tough-guy act is wearing thin.

Elected with 38 percent of the vote in a five-way race amid a Tea Party wave, LePage has become one of the most endangered incumbent governors in the country, with low voter popularity and a slight deficit in the polls.

His defenders say that, as a former manager of a discount chain, he represents workaday Mainers who want lower taxes and smaller government. Democrats and other opponents say he is bent on gutting the safety net for the poor, as they attempt to portray him as an embarrassment to the state. Even some Republicans agree he is a polarizing figure.

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“There’s no ‘somewhat,’ in terms of the governor. He’s so divisive that people have very strong opinions,” said Dan Demeritt, a former LePage aide and sometime critic who now works as a political consultant. “He turns the race into a LePage referendum.”

LePage’s vulnerability could create an opening for a historic candidacy. US Representative Michael H. Michaud, a low-key Democrat from a paper mill town in the north, would become the nation’s first governor to declare he is gay before being elected, if he wins in November.

The combination of LePage’s weakness and Michaud’s potential to break new ground has already drawn an unusual level of national interest in the campaign. Michaud got top billing at the Victory Fund’s National Champagne Brunch Sunday in Washington, a fund-raising event for a group that seeks the election of gay candidates.

LePage — who has a testy relationship with the media and declined to be interviewed — is hoping for a repeat of 2010, when moderates and liberals were divided among multiple candidates, allowing LePage to squeak into the governor’s office with a narrow plurality. A key ingredient from that race is back: Eliot Cutler, an attorney who once worked for Senator Edmund Muskie and Jimmy Carter, is running as an independent candidate and says he will stay in the race to the end.

Democrats are attempting to coalesce around Michaud early and halt any momentum for Cutler. Strategists and politicians from across the spectrum say Cutler is unlikely to repeat his strong showing from 2010, when he surged to within two percentage points of victory.

Regardless of who emerges as LePage’s biggest threat, President Obama’s health care law is expected to play a prominent role in the runup to the election. LePage campaigned against the law in 2010 and has steadfastly refused to adopt its offer of generous federal financial help to expand Medicaid. Michaud and Cutler both support the Medicaid expansion, as do a narrow majority of voters, according to the most recent poll by Pan Atlantic SMS Group, taken in late November.

The poll showed LePage is highly unpopular personally: 43 percent of voters view him favorably compared with 54.5 percent who hold an unfavorable view. By contrast, Senator Susan Collins, his fellow Republican and the state’s most popular politician, is viewed favorably by 78.5 percent of voters.

The poll showed Michaud with a 1 percentage point lead over LePage, similar to other polls of the race.

LePage’s supporters concede his brash behavior has made his future more difficult. They say he has yet to adapt to the political world and his intentions are misunderstood. He came from a troubled background, the oldest boy in a family of 18 children, and his childhood included bouts of homelessness.

“The governor’s very direct in what he’s thinking and sometimes that doesn’t come out in the best ways,” said Michael Thibodeau, the top Republican in the state Senate. “Someone said to me the other day, ‘I’d rather have Paul LePage with his foot in his mouth than a slick politician with his hand in my pocket.’ ”

‘The governor’s very direct in what he’s thinking and sometimes that doesn’t come out in the best ways.’

LePage supporters cite results of his administration: retiring hundreds of millions of dollars in Medicaid debt to the state’s hospitals, a $200 million income tax cut, an overhaul in the public pension system, and fewer regulations. He has also been pushing an extensive plan to reduce welfare costs.

Ray Richardson, a conservative radio host who has been a key ally since LePage’s last election, said the governor has enough strong supporters to win a three-way race.

“I wish he were a little more careful,” Richardson said. “On the other hand, when he starts being careful, he stops being effective. We have far too many pretty boy politicians who don’t get a damn thing done.”

LePage has vetoed a record number of bills, 127, since he took office. That number accelerated after Democrats took control of the Legislature in 2013. Democratic state leaders say they seldom meet with LePage. And when they do, he often punctuates his opinions by pounding the table or cutting meetings short.

“He has at times struggled with the concept that he’s got 186-member board of directors,” said Roger Katz, the second-ranking Senate Republican.

Troy Jackson, a Democratic senator and logger,
was more direct. LePage lashed out at Jackson last year with a graphic phrase after he criticized the governor’s budget. “He’s a dictator that dislikes anyone challenging anything that he has to say,” said Jackson. “Those regimes don’t normally last long.”

Democrats argue that LePage’s $200 million income tax cut skewed toward the wealthy and led to an indirect property tax hike at the local level. Decreases in income and estate taxes, which LePage signed in 2011 before Democrats gained control of the Legislature, saved Maine’s top 10 percent, or families earning more than $120,000 a year, the most money, according to state revenue statistics. But families with lower incomes saw their tax bills decline by a greater percentage.

Most of all, Democrats want to put LePage’s personality front and center in the election. They say LePage is sullying Maine’s national reputation, drawing unflattering attention to a state whose residents are typically known for their tact and personal discretion.

“When people think of Maine, we want them to think of our coastline and our lobsters and our blueberries,” said Democrat Mark Eves, the House speaker. “We do not want them to think about a belligerent governor who doesn’t represent our values.”

Michaud has worked to get early endorsements from a spectrum of interest groups to build the sense that he is the only alternative to LePage. Many Republicans agree that Michaud appears to be a stronger candidate than Libby Mitchell, the Democrat who finished third in 2010, and that Cutler has yet to gain traction.

Though Michaud is 59 and was elected to the Maine Legislature 34 years ago, he only came out as gay in November, to head off what he called “whisper campaigns” intended to take down his candidacy.

“Yes I am. But why should it matter?” the former paper mill worker wrote in a column published in several state newspapers.

Voters and opponents seem to agree. It has not been a significant issue in the campaign. The state, once seen as hostile to gays, approved same-sex marriage in a ballot referendum in 2012.

In an interview at his campaign consultant’s office in Washington, Michaud was as mild as LePage is bombastic. He talked about the importance of his announcement in the lives of people who have since reached out to him but downplayed its effect on voters.

“It definitely is historic,” he said. “That’s not why I ran for governor. My sexual orientation never played a role in how I did my job when I worked 29 years at Great Northern Paper Company. It never affected how I made my decisions as a member of the Maine Legislature or in Congress. And it definitely won’t affect how I operate as governor.”

Cutler is the wild card in the race. He is criticizing both political parties. He challenges Michaud’s past votes against abortion rights, environmental regulations, and even gay rights. He says LePage has failed to improve the state’s struggling economy, failed to manage the government, and, because of his combative demeanor, failed to get anything done.

Michaud, whose base of support is from the conservative northern region, said his positions on social issues — including gay rights — evolved along with his constituents’ views. But he was eager to change the subject to LePage.

“The fact that Maine has been on the late-night TV shows — because of our governor — is disconcerting,” he said.

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